Windows 7 64bit will run most software released since 2000. I've had some trouble with software from 1999 and older, but a lot can still be made to work even that old. And you have xp mode, which runs a version of virtual PC and a full copy of xp in a virtual machine, and programs running within this run in a window just like a native program.
Don't consider the 64bit version of Windows 7's compatibility to be anything like XP's was. That was terrible at running many programs, and hardly any games. But from 64bit Vista onwards compatibility between the 32bit and 64bit versions of Windows have been nearly identical. You will only find a few programs with issues, and in recent years many developers are focusing more on the 64bit builds.
The main advantage of 64bit is access to more system ram for the OS. Even a basic system these days should have at least 4GB ram, and you need a 64bit OS to see and use all of it, so the 64bit version is really a must, especially as system with 8GB or more will be a smoother and faster experience. For games, more ram isn't such an issue, but for any productivity software, such as Photoshop or video editing, the more ram the better.
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